Blender 2.8x - Particle Color based on actual color of emitter
Thanks to @Lumpengnom at https://blenderartists.org/ 
I found the solution!

Important steps are:

1.) Add a texture coordinate node, connect UV to vector and enable the "from Instance" check-mark.

2.) Use Cycles renderer, also for preview!, otherwhise you will not so the right result which is very irritating.

Here is a quick video tutorial:
https://youtu.be/8W1J8hYjK9g